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Matteo Cantiello edited Mode Visibility.tex
over 8 years ago
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\end{equation}
where $r_1$ and $r_2$ are the lower and upper boundaries of the evanescent zone, respectively. The fraction of wave energy transmitted through the evanescent zone is $T^2$. For waves of the same frequency, larger values of $\ell$ have larger values of $r_2$, thus Eqn. \ref{eqn:integral2} demonstrates that high $\ell$ waves have much smaller transmission coefficients through the evanescent zone.
The visibility of stellar oscillations depends on the interplay between driving and damping of the modes \cite{Dupret_2009,Benomar_2014}. To estimate the reduced mode visibility due to energy loss in the core, we assume that all mode energy which leaks into the g mode cavity is completely lost. The mode then loses a fraction $T^2$ of its energy in a time $2 t_{\rm cross}$, where $t_{\rm cross}$ is the wave crossing time of the acoustic cavity. Due to the larger energy loss rate, the mode has less energy $E_{\rm ac}$ within the acoustic cavity and produces a smaller luminosity fluctuation $V$ at the stellar surface, whose amplitude scales as $V^2 \propto E_{\rm ac}$. We show
\cite{supplementary} (supplementary material) that the ratio of visibility between a suppressed mode $V_{\rm sup}$ and its normal counterpart $V_{\rm norm}$ is
\begin{equation}
\label{eqn:vis}